Question 19588: In this problem you are asked to convert the general standard form of a quadratic polynomial into the completed square form. Suppose f(x)=Ax^2+Bx+C where A,B, and C are the coefficients of the quadratic polynomial, and A does not equal 0. then F can be written as f can be written as f(x=a(x-h)^2+k where
a= A
h=
k=
Enter your answers as algebraic expressions in A,B, and C.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! In this problem you are asked to convert the general standard form of a quadratic polynomial into the completed square form. Suppose f(x)=Ax^2+Bx+C where A,B, and C are the coefficients of the quadratic polynomial, and A does not equal 0. then F can be written as f can be written as f(x=a(x-h)^2+k where
a= A
h=
k=
Enter your answers as algebraic expressions in A,B, and C.
we have .....f(x)=Ax^2+Bx+C =a(x-h)^2+k=a(x^2+2hx+h^2)+k=ax^2+2ah*x+a*h^2+k
this is an identity so corresponding terms on either side of = should be same...so....
Ax^2=ax^2...and...Bx=2ah*x...and...C=a*h^2+k..or
A=a....and.....B=2ah....and....C=a*h^2+k
so a=A..and..h=B/2a=B/2A...and.....k=C-A*(B/2A)^2
|
|
|
